Algebra : Set Theory

[introduction][ common sets ][ Venn diagrams ][ sub-sets]






A set is a collection of objects, numbers or characters.

{abcdef....wxyz}  {1,2,3,4,...45, 46, 47}   etc.

Note how the set is enclosed in brackets {.....}

A definite set is one in which all its members are known.

Sets are given uppercase letters: A, B, C, etc.

The elements of sets are given lowercase letters: a, b, c,..etc.

An element x belonging to the set A is written:

x is an element of the set A

A constraint bar {...|...} is for setting a property that all members satisfy.

A{x l x has the colour blue} - all elements of A are blue


Common Sets

set types


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Venn Diagrams

Venn diagrams are used to visualise sets and their relations to one another.

venn diagram#1

Above is a diagramatic representation of set A. The set can be represented mathematically as: A{1,3,5,7,9} .

Note that set A(the circle) is a subset of the Universal set(the rectangle).


venn diagram complement

A' (A-dash)is called the complement of A. It contains all elements which are not members of A.

A and A' together make up the Universal set.



The union of sets A and B contains all of the elements from both sets.

union of sets



The intersection of sets A and B contains a particular group of elements that exist in set A and in set B.



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If B is a subset of A. Then all of the elements of B are also in A.

venn diagram B is a subset of A

B is a subset of A




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parametric differen.
equation of a tangent
equation of a normal
rate of change prob.1
rate of change prob.2
the Chain Rule
Chain Rule probs. #1
Chain Rule probs. #2
Chain Rule probs. #3
the Product Rule
parametric eqs.prob#1
parametric eqs.prob#2
intro. to integration
integration by parts 1
integration by parts 2
area under a curve
volumes of revolution
area between curves
Binomial Theorem
Bin. Theorem problems
Trig. Identities
Half Angle Formula
Double Angle Formula
Vector problems
Vector problems in 3D
MORE . . .


derivative formula
tangents & normals
inverse functions
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Edxl C1 Pure specimen
Edxl C1 Pure answers
Edxl C2 Pure specimen
Edxl C2 Pure answers
Edxl C3 Pure specimen
Edxl C3 Pure answers
Edxl C4 Pure specimen
Edxl C4 Pure answers
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the derivative formula
tangents & normals
maxima & minima
chain rule
diffn.trigonometric fns.
product rule
quotient rule
parametric equations
implicit equations
differential equations
integration formula
int.'by substitution'
int.'by parts'
algebraic fractions
definite integrals
areas under curves
volumes of revolution
Trapezium Rule
integ. diff. equations
sine, cosine, tangent
sec, cosec, cotan
Sine & Cosine Rules
Pythagorean ID's
compound angles
Sigma Notation
arithmetic progression
geometic progression
line between points
more straight lines
parametric equations
circles & ellipses
MORE . . .